All committed relationships require giving up doing things that you want to do for the sake of your love for the other person. It doesn't really matter that you find yourself attracted to other people of the same sex or the opposite sex. Since your BF is not interested in sharing you with other women, you will need to decide if he is worth giving up on your urges.
Are there other problems in your relationship? Sometimes a wandering eye is just a way to break out of a bad relationship or get attention from others that you are lacking at home. Since you said this is a new problem, what happened when you started to have fantasies about other women?